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 Monday, May 28, 2007 #7339

What is the "Sainsbury" formula and is there a difference between unique circulation and paid circulation? Thank you!
 The Media Guru Answers(Monday, May 28, 2007 ):

The Sainsbury formula is a method for combining the reaches of schedules in different media. It varies from the simple random probability method which is based on the generally accepted assumption that there is no particular correlation between exposure to one medium and another. Sainsbury varies by adding a small adjustment to account for an assumed slightly morethanjustrandom probability that those exposed to an advertiser's schedule in one medium will also be exposed to its schedule in the next medium. Typically, the adjustment is about a 5% deduction from the result of the random combination.
As you will see at the link shown, we may vary in our arithmetic expression of the probability equation (for the same result), so we can express the Sainsbury formula as (0.95 x random probability).
Unique circulation and paid circulation are unrelated terms.  Paid circulation refers to the number of copies which are actually bought for money at the newsstand or by paid subscription, rather than distributed free or at such a discounted rate that the circulation auditor no longer qualifies the copies as "paid."
 "Unique" is more commonly an intrnet audience term. Perhaps you are thinking of "unduplicated" audience which only counts readers once, if they read two or more issues.
 Wednesday, April 04, 2007 #7309

Who is the founder of random Media combination theory? Thank you
 The Media Guru Answers(Wednesday, April 04, 2007 ):

The Guru would not consider this a "theory" per se, nor that there is a "founder."
The "random" concept is basic statistics: when the probablity of occurrence of two unrelated phenomena is known, then the probablity of both occurring is calculated by the product of the two probabilites. In media terms, this means:
Multiplying the two reaches together gives the probability of both reaching the target, which is not reach, but duplication.Of course, the reach of different media schedules reaching the same target are not truly unrelated phenomena, and various adjustments to pure random have been promulgated by many practitioners.
 Friday, June 29, 2001 #4538

Hello again,
I have two questions about calculating reach and frequency that I have been unable to find in the archives of past responses. Perhaps you can help?
1. I normally use the formula (a+b)(.a*b) to determine combined reach of two mediums, such as radio and print. How do I calculate the combined reach of more than two? The plan I am working on includes spot TV, spot radio and local newspaper.
2. Is it possible to determine a combined reach for more than one market or should each market be reported separately? In the past, I have provided separate delivery for each market in the same plan with a total number of gross impressions for the whole plan. Is this correct?
Thanks in advance!
 The Media Guru Answers(Friday, June 29, 2001 ):

1. This common formula is based on an assumption that different media duplicate their audiences according to random probability. Therefore if you follow this assumption, media may be added to combinations of media in a "chain" of the same formula. So, once you have combined TV and Radio, you can use this combination as your "a" and then combine it with newspaper as "b."
2. You can combine reaches across markets by doing a weighted average. Multiply the reach in each market by the percent of U.S. in each market. Add all the products and divide by the sum of the % U.S.
 Friday, May 04, 2001 #4368

Media Guru, please help. How do I calculate reach and frequency for a twoweek, twonewspaper buy? We are placing 4 ads per week (total of 8 ads for the schedule) on Newspaper #1, which has a maximum reach of 9% of our target. Newspaper #2 will carry 2 ads per week (4 ads for the schedule) with a maximum reach of 23% of our target. Please advise. Thanks!
 The Media Guru Answers(Sunday, May 06, 2001 ):

Find some example newspaper R&Fs at The Newspaper Advertsing Associations Marketscope site.
In very general terms, you can estimate some parameters. If newspaper A has a 9% maximum reach, it probably has a single copy reach of around 7%. If B has a maximum of 23%, then it likely has single copy reach around 20%. So the outside bounds of reach for your schedule are a minimum of 20, but more likely closer to 25, the random combination of the two papers' single copies. The outside maximum is 32 ( the 9% plus the 23% maxima), but more likely closer to 30 (random again).
A solid estimate of 2530 reach for your schedule should be good enough, but you could use the eTelmar payperuse system for a specific calculation.
Frequency, of course, will be the sum of the single copy audeinces of all insertions (GRP) ÷ the reach estimate.
 Thursday, March 16, 2000 #3326

Dear Guru:
I would like to know if there is any equation to calculate media mix reach?
 The Media Guru Answers(Thursday, March 16, 2000 ):

There are several, equivalent ways to express the arithmetic to combines media according to random probability, which has been found generally adequate for the purpose of multimedia combination.
Here's an easy one:  Work with two reaches at a time
 Treat the reach of each medium as a decimal (50 reach is 0.5)
 Add reach of medium A and medium B
 Multiply reach of medium A by Reach of medium B
 Subtract the product of the multiplication from the sum of the addition
Example:  Reach of medium A = 40, reach of medium B = 55
 0.4 + 0.55 = 0.95
 0.40 x 0.55 = 0.22
 0.95  0.22 = 0.73
 Combined reach is 73
To add additional media, treat the combination as medium A and the next medium as B.
In some cases, a planner may have access to research which shows that an adjustment should be made for actual, measured, duplication between different media, rather than use the "random probability" formula above. In that case, more sophisticated reach calculating software packages, such as those from
Telmar allow you to make the calculation and build in known adjustments.
 Tuesday, September 14, 1999 #2792

What can you tell me about reachbased planning?
Thank you in advance.
 The Media Guru Answers(Tuesday, September 14, 1999 ):

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The usual assumption is that print and broadcast duplicate with random probability, there is no special, greater or lesser likelihood that persons in the audience of the print schedule will also be or not be in the audience of the broadcast schedule.
Mechanically. the combination may be calculated in a few equivalent ways. The Guru finds it easiest to consider the reaches as decimals (50% reach = 0.50). Subtract the reach of print from 1 and multiply this by 1minus the reach of broadcast. Suppose print has a 40% reach and broadcast has 55%. By subtracting 0.4 from 1 (1  0.4 = 0.6), you have the probabilty of the target not being exposed to print. Subtract 0.55 from 1 to get the probability of not being exposed to broadcast (1  0.55 = 0.45)
Multiply these two together (0.6 * 0.45 = 0.27) and you have determined there is a 27% probability of people not being exposed to either of the combined media, or a 73% reach.
This formula is typically used in media software to combine different media. Certainly there are cases where there is a somewhat better than random probabilty of media duplication, such as TV Guide combining with a TV schedule, but that's the exception, calling for judgement.
 Wednesday, September 01, 1999 #2759

Is the random probability formula used to combine reach for different media also valid when looking at effective reach (i.e. 4+ level)?
 The Media Guru Answers(Thursday, September 02, 1999 ):

If you mean, can you combine the 4+ reach of one medium with the 4+ reach of another medium to get the 4+ reach of the two combined media, the answer is no.
Among those who were reached 2 or 3 times by each medium, some will now be reached 4 or more times and some will not, yet these people are not considered by combining only the two four+ groups. There are also those reached only once by the first medium and three times by the other, etc. A new, overall calculation of the frequency distribution must be done, to determine the 4+ of the combination.
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